Non-linear potentiometer



July 24, 1962 D. G. WILLIAMS ET AL NON-LINEAR POTENTIOMETER Filed Aug.18, 1961 3,046,510 Patented July 24, 1962 3,046,510 NON-LINEARPOTENTIOMETER David G. Williams and Joyce W. Williams, Littleton, Mass.,assignors to Ace Electronics Associates, Inc., a corporation ofMassachusetts Filed Aug. 18, 1961, Ser. No. 132,322 9 Claims. (Cl.338-89) The present invention relates to variable resistors, such aspotentiometers and rheostats, and is concerned primarily with resistancecards for use in such variable resistors.

` United States Patent Oce In particular, this invention relates toresistance cards f adapted to provide non-linear voltage functions,rsuch-as sine and cosine functions, when traversed over the surface by awiper tap along a circular curve having as its center the center of thecard.

It is recognized in the prior yart that a fiat square resistance card,whether wire wound, or formed of a molded resistance material, or formedby a deposited layer of resistance material, may be utilizedftoprovidesine-cosine output voltage functions; and one may vobtain such outputslby imposing a uniform voltage across the card from contacts mounted forunison rotation on `a single shaft.

Itis apparent that Vthe most eliicient manner of ganging a plurality ofthese potentiometers is to mount a shaft through the centers of theseveral resistance cards, and to mount on the shaft a variablepotentiometer wiper con- .tact arm for each card adjacent 'to theresistance surfaces of the respective cards. The resultant holes in thecards to accommodate the shaft afect'the voltage and currentdistributions over their surfaces, and thereby destroy or distort thesine-cosine functions originally obtainable yby circular traces or wipesabout `the centers of the cards. The art has recognized the existence ofthis problem, and has sought through various means VAto correct `forthese deviations, `as by altering the configuration of the card inputterrninalsrapplied along twoi opposite edges of the card (RosenthalPatent 2,764,657), or by altering the configuration of the two oppositecard edges transverse to the input terminal edges of the card(Montgomery Patent 2,653,206);

These proposed `solutions to the problem, however, have been onlyapproximations, and have failed to grasp the basic nature of theproblem. `Arhole inthe center of a square resistance card alters thevoltage and current distribution over the area of `the card so that theequipotential lines, which originally were straight lines across thecard parallel to the voltage input edges of they card, are no longerstraight, and differ in configuration at different ,points Vbetweenthevoltage input edges. This compound ..mensions, i.e. along thedimensions parallel to and perpen- .v

hole through its center. It has'been found that allfour edges oftheresistance card should follow complex curves.

For a card having a round hole through itscenter, it has been found thatthe two opposite edges of the-card generally paralleling theequipot'ential lines across the U 2 card, i.e. thetwo card edges alongwhich the voltage input terminals are applied, should be generallyconcave; whilethe opposite twoedgesof Ithe card, the orthogonaltrajectories, should be generally convex. More specifically, theequipotentialk edges should lfollow `a curve defined by the formula K K2sin2 1 wherein r is the'dis'tance from the center of the card forvarious angles qi about the center, a is the radius of the round holeformed in the center of the card, and K is a constant; and theorthogonal trajectory edges should follow a curve defined by the formulawherein r, qs, and a are stated above, and C is a constant. Accordingly,it is oneV object of the present invention to provide a resistance cardadapted for use in a sinecosine potentiometer. Another object of thepresent invention is to pro` vide such a card having a -hole in themiddle to facilitate ganging a plurality of sine-cosine potentiometers,

Still another object of the present invention is to provide asine-cosine potentiometer formed from such a card and having a variabletap mounted on -a rotary shaft passing through said hole.

And a further object of the present invention is to provide a pluralityof such sine-cosine potentiometers ganged on a common rotary lshaft forthe variable tap of each potentiometer. ,f f

Other lobjects and advantages `of the present invention.

|will become apparent tothose skilled in the art from a consideration ofthe following detailed description of one exemplary specific embodimentof the present invention, had in conjunctionwit'ht-he `accompanyingdrawings,

wherein like numerals refer to ylike or lcorresponding parts,

and wherein: y n

FIG. l is a plan view ofa flat resistance card formed in accordance withthe present invention;

FIG. 2 is a longitudinal sectional view of la plurality of gangedpotentiometers, each incorporating aL resistance card as shown in FIG.l; and

FIG. 3 is a cross-sectional View of the ganged potentiometers of FIG. 2,ktaken along the line 3--3` thereof.

The flat resistance card of the present invention-is indicated generallyby the numeral 10. Preferably this card is formed as va moldedconductive plastic resistance, and is of uniform cross-sectionalthickness so as to provide substantially uniform specific resistivityover its extent. For structural support and mounting purposes, the card10 is united to an insulating discr 11, which may also be a plastic, by'any suitable means such as `a resinglue or`=adhesive, or by comolding.Conductiveterminal strips 12 and 13 are applied along opposite vedges 14and 15 of the resistance card, and may be applied as conductive coatingson the resistance card, or laminated thereto as preformed conductivemetal foils, or comolded with the card 410 as conductive metal terminalplates. A hole 16 is formed in the center of the card 10 and overlies ahole 17 of smaller diameter in the insulating disc 11. t n i Leads froma voltage source (not shown) are to bel applied to terminal strips 12and 13, thereby establishing a voltage gradient across the resistance`card 10 .between these terminals.. A variable potentiometer Wipercontact, to be subsequently described, mounted on a shaft passingthrough holes 16 `and 17is intended to traverse the surface ofresistance card 10 along ya circleindicated for example Eby the phantomline 18. In traversing the circle 18,

3 the variable contact taps an output voltage from the card varying inaccordance with a sine-cosine function, one complete sine-cosine cyclefor each 360 of traverse over circle 18.

In order to produce a substantially true sine-cosine output function,edges 14 and 15 of the card, referred to herein as the equipotentialedges, followaa generally concave curvature, while the other two edges19 and 20` follow a generally convex curvature. More specifically, asubstantially pure sine-cosine output function is obtained when thecurvature of edges 14 and 15 follows the curve defined by the equationand the curvature of edges 19 land 20 follows the curve dened lby theequation wherein r is the distance from the center of the card (pointZ1) for various angles gb about said center, C and K are constants, anda is the radius of hole 16.

In order that the nature of the present invention will be more fullyappreciated, the mathematical derivation of the foregoingequations ispresented. The Ifollowing derivation and the foregoing equations applyto a flat resistance card of uniform specic resistivity, having a hole16 of radius a in the center .of the card :about point 21. The circularwiper track `18 is concentric with lthe hole and has a radius b.

Let

Vr=b=F sin el (1) where V is la voltage function, t the displacementangle `about the center of the card and r is a distance from the centerof the card along a radius vector. Then Assuming VU, =R(r) I 15) Inpolar coordinates WeaaearsaetarLira RU) E dr @((b) =a constant--m2 LetB21 which is the Asolution for the curvature of edges 14 land 15.

From Equation 19,

is the differential equation for the orthogonal trajectories, whenequated to Equation 30 is the solution for the curvature of edges 19 and20.

Referring to FIGS. 2 and 3, the resistance card of FIG.

1 is shown assembled in a potentiometer, and two such J pg 1,).

hub portion S0 which substantially surrounds the shaft 30, and yfromwhich extend a wiper arm support 33' and two clamping legs 34. A yscrew35 threads into the two legs 34 and operates by compressing the legs 34to clamp theannular portion about the shaft. A split sleeve 31 ofinsulating material is interposed between the annularl portion 5,0 ofthe wiper assemblyrand the shaft 30, to isolate the shaftelectricallyfrom the Wiper assembly.

The end of the wiper arm support 33 is split at 38 and an end of4contact element 39 Vis soldered therein. The contact element 39 extendsfromrthe'arrn 33 and is bent at 40 to resiliently engage the surface 10aof resistance card 10.` Thus, when shaft is rotated, the'assembly 32 isrotated therewith,A causing portion 4G` of wiper contact element 39 totraverse the surface 10a of card 10 in a circular path.

An annular slip ring 36 is spot welded to hub S0 in an area adjacent thearm 33, leaving split hub 50 resiliently contractable by compression oflegs 34 for clamping purposes. A peripheral groove 37 is formed aboutthe annular slip ring 36 to accommodate a brush, usually in the form ofa resilient wire lead. The entire wiper contact assembly 32 is made ofelectrically conductive metal, so that a voltage tapped at 40, may beobtained at the slip ring 36.

For the purpose of simplifying the illustration, the input and outputleads have not been shown. However, it is understood that leads may beconnected to terminal strips 12 and 13 to develop a voltage drop acrossthe card 10. An output is derived from a lead slidably engaging thegroove 37 in slip ring 36, and this output voltage will vary inaccordance with a sine-cosine function as the wiper tap 40 is caused totraverse a circular path about the axial center of shaft 30 over thesurface 10a. of card 10.

As previously stated, the wiper assembly 32 is clamped to the shaft 30by means of screw 35 and clamping legs 34. The assembly 32 is locatedaxially along shaft 30 to bring the wiper tap 40` into resilientengagement with the surface 10a of card 10. The wiper assembly andresistance card are preferably separated by an insulating spacer 42, andthe entire assembly'is backed by a split ring 43, seated in acircumferential groove defined about shaft 30 to bear against the backof plate 11. Suitable bushing may, of course, be provided between shaft30 and ring 43 and plate 11, if desired. A plurality of suchpotentiometer assemblies may be mounted on shaft 30, two being shown forillustration purposes in FIG. 2, and of course their wiper contacts maybe phased to any angle of rotation relative to each other.

The potentiometers thus assembled on shaft 30 are mounted in a housing46, which may comprise a cupped tubular body 46a having an aperture 4-9`in its bottom wall, and an axial slot or key way 48 along its tubularwall. Each plate 11 is provided with a key 41 which locates in key lway48 to register the resistance cards and retain them against rotation. Anend of shaft 30 is seated in the hole 49 in the bottom wall of thehousing. A

cover cap 47 having an aperture 50 is applied over the open end oftubular body 46a to close the housing 46, and support the protruding end45 of lshaft 30. The shaft is locked in axial position by means of twosplit rings 44 seated in circumferential grooves in shaft 30 and bearingagainst the exterior of the two ends of housing 46.

Thus, shaft 30 may be rotated by means of its protruding end 4S, causingthe gangedwiper assemblies mounted thereon to rotate therewith, whilethe resistance cards are restrained against rotation by the keys 41located in key Way 48. With resistance cards 10` fashioned in the manneraforedescribed, andwith desired voltages applied across the cards,rotation of shaft 30 obtains sine-cosine function voltage outputs fromthe wiper taps an-d assemblies 39 and 32.

There is thus provided by the present invention a fiat 6 resistance cardhaving a circular hole in rits center, and formed to generate asine-cosine voltage output, when energized in a potentiometer circuitand, traversedinva circularl path by a wiper tap. Because of thecircular hole, a plurality of such cards may be mounted over av bracedby the spirit and scope of the appended claims, are

contemplated as within the purview of the present invention.

What is claimed is:

1. A potentiometer comprising a resistance card, said card having a holein the center thereof and four peripheral edges, a terminal stripapplied along the length of each of two opposite ones of said four edgesfor establishing a voltage gradient across the face of the card betweensaid two opposite edges when a voltage is applied to said terminalstrips, said two opposite edges being shaped with a generally concaveperimeter curvature, and the other two of said four peripheral edgesbeing shaped with a generally convex perimeter curvature, a rotationalshaft passing through said hole, a wiper tap supported by said shaft fortraversing the surface of said card in a circular parth about said hole,and means for supporting said shaft and card for relative rotation aboutthe axis of said hole.

2. A potentiometer as set forth in claim l, wherein said hole iscircular and its center is the center of said card, said card hassubstantially uniform specific resistivity over its extent, theperimeter of said card is completely defined by said four edges, saidcurvature of said two opposite edges is defined substantially =by theequation:

and said curvature of said other two edges is defined substantially bythe equation:

wherein r is the distance along the radius vector from said center forany angle of rotation qb about said center, a is the radius of saidhole, and K and C are constants,

l whereby a sine-cosine function voltage output is tapped by said wiperwhen caused to traverse the surface of said card in a circular pathabout said center.

3. A potentiometer as set forth in claim 2, wherein said card is a thinsubstantially flat card.

4. A potentiometer as set forth in claim 2, comprising a plurality ofsaid cards, said shaft passing through the hole in each said card, and avariable wiper tap for each said card supported by said shaft.

5. A potentiometer as set forth in claim 3, wherein said card is aconductive plastic material.

6. A resistance card adapted for use in a potentiometer, having fourperipheral edges and a hole in the center thereof, a terminal stripapplied along the length of each of two opposite ones of said four edgesfor establishing a voltage gradient across the face of the card betweensaid two opposite edges when a voltage is applied to said strips, saidtwo opposite edges being shaped with a generally concave'perirnetercurvature, and the other two of said four peripheral edges being shapedwith a'generally convex perimeter curvature.

7. A resistance card as set forth in claim 6, wherein said'hole iscircular and its center is the center of said and said curvature of saidother two edges is deiined substantially by the equation:

wherein r is the distance along a radius vector from said center for anyangle of rotation p about said center, a is the radius of said hole, andK and C" are constants,

whereby a voltage output tapped from said card by a circular trace aboutsaid `center varies as a sine-cosine function when a uniform voltage isvapplied to said terminal strips.

8. A resistance card as set forth in claim 7, wherein said card is athin substantially flat card.

9. A resistance card as set forth in claim 8, wherein said card is aconductive plastic material.

References Cited in the tile of this patent UNITED STATES PATENTS2,457,178 Richardson et al. Dec. 28, 1948 2,542,478 Clark Feb. 20, 19512,648,752 Saunders Aug. 1l, 1953 2,653,206 Montgomery Sept. 22, 1953

